 | William Enfield - Astronomy - 1832 - 282 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the baseRSM, RMS, is to the tangent of half their difference. Tohalfthe sum add half the difference, and... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...tan. i (A + B) a — b ~ "tan. i ( A — B j ' that is to say., in any plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By help of this rule we may determine the... | |
 | Euclides - 1834 - 518 pages
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in to their difference, as the tangent of half the sum of the angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at... | |
 | Euclid - 1835 - 540 pages
...half the difference, and it will give the less. PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides AB,... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. * PROP. IV. F1G. 8. In a plane triangle, the cosine ofhalftke... | |
 | Adrien Marie Legendre - Geometry - 1836 - 382 pages
...b + c=2p; we have a + 6 — c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem... | |
 | John Playfair - Geometry - 1836 - 148 pages
...triangle, any three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides, AB,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...sine of a right angle is equal to the radius. PROP. III. THEOR. THE sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, is to the tangent of half their difference. Let ABC be a triangle, a, b any... | |
 | Charles Davies - Navigation - 1837 - 342 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
